Time Speed and Distance Quiz-1

Since the train and Rahul Gandhi are moving in opposite directions,

The relative speed = 60-(-6) kph = 60 + 6 = 66 kph

66 km/h in m/s = 66 \times \frac{5}{18} = \frac{55}{3} m/s

Total distance to be covered = 110 m (length of the train)

So, time = \frac{distance}{speed} = 110 divided by \frac{55}{3} which equals 6 s.

So, the required time is 6 seconds.

Let the length of the train be L metres

Speed of first train = \frac{L}{\frac{18}{3600}}=\frac{3600\times L}{18}= 200L m/hour

Speed of second train = \frac{L}{\frac{12}{3600}}=\frac{3600\times L}{12}=300L m/hour

When running in opposite directions, relative speed = (200 L + 300 L)= 500L m/hour

Distance to be covered = L + L = 2L metre

Time taken = \frac{2L}{500L}\times 3600=14.4 sec

Let length of train be x m.

Speed = \frac{x+100}{25} = \frac{x}{15}

=> 15(x + 100) = 25x

=> 15x + 1500 = 25x

=> 1500 = 10x

=> x = 150 m.

Given speed = 63 km/hr = 63 \times \frac{5}{18} = \frac{35}{2} m/s

Let the length of the bridge = x mtr

Given time taken to cover the distance of (170 + x)mts is 30 sec.

We know speed = \frac{distance}{time} m/s

⇒ \frac{35}{2} = \frac{170+x}{30}

⇒ x = 355 mtr.

Let the speed of stream = x
Sunny deol’s Speed = 4.5
Upstream Speed = 4.5 - x
Download Speed = 4.5 + x
Downstream Time : Upstream Time = 1 : 2
Downstream Speed : Upstream Speed = 2 : 1
(4.5 - x)/(4.5 + x) = 1/2
9 - 2x = 4.5 + x
3x = 4.5
x = 1.5

Let the distance travelled by each car be x
Abhishek travels half distance = 40kmph
Another half distance = 60kmph
Time taken in 1st half = x/40
Time taken in 2nd half = x/60
Avg. speed = total distance/ total time
= x+x / t1 + t2
= 2x / x/40 + x/60
= 4800x / 100x = 48 kmph

Let the speed of the cyclist be x km/h and wind be y km/h

⇒ <br /> <br /> ⇒ x + y = 20..........(i)<br /> <br /> And, \frac{1}{x-y} = \frac{4}{60}

⇒ x - y = 15.........(ii)

On solving both the equations we get:

x = \frac{35}{2}     &     y = \frac{5}{2}

Now, time taken by cyclist without wind: \frac{2}{35} \times 60 = \frac{24}{7}min

Let the speed of the stream be x km/hr. Then,

Speed downstream = (15 + x) km/hr,

Speed upstream = (15 - x) km/hr.

∴ Total time taken = \frac{30}{15+x} + \frac{30}{15-x}

\Rightarrow \frac{30}{15^2-x^2}=\frac{4.5}{30}\ \ \Rightarrow 15^2-x^2=200

⇒x² = 25 km/hr

⇒ x = 5 km/hr.

Let the speed of the goods train be x km/hr
Relative speed =(50+x) km/hr =(50+x)×185​ m/s
Therefore, (50+x)×5/18187.5​=9
⇒250+5 / 187.5×18​=9
⇒250+5x = 187.5×2 = 375
⇒5x = 375−250 = 125
⇒x= 25 km/hr

Speed of boat downstream = \frac{Distance covered}{Time taken} = \frac{30}{2} = 15 km/h

Now, speed of boat upstream = \frac{Distance covered}{Time taken} = \frac{30}{6} = 5 km/h

Now, speed of boat = \frac{Speed downstream+Speed upstream}{2}

= \frac{15+5}{2} = \frac{20}{2} = 10 km/h